Effects of Gamma-Distribution Variations on SPI-Based Stationary and Nonstationary Drought Analyses

Abstract

This study aims to analytically explore the effects of changing rainfall distributions in terms of variations in the mean and variance of gamma distributions on the drought analysis based on standardized precipitation index (SPI). Traditional SPI calculation involves the fitting of observed rainfall series to a time-invariant probability distribution; the gamma distribution is commonly used. Fitting a time-varying gamma distribution to a trending rainfall series leads to nonstationary SPI (NSPI) series. The effects of changing gamma distributions on the SPI and NSPI can be systematically summarized by the proposed nine-category distributional-change scheme in terms of variations in the mean and variance of the gamma distributions. The annual wet-season rainfall series at Taipei (1897–2017) and Dawu (1940–2017), which exhibit significantly increasing and insignificantly decreasing trends, respectively, were selected for demonstration. A clearly increasing rainfall trend at Taipei over the last four decades corresponds to less severe droughts in the SPI series and more frequent and more severe droughts in the NSPI series. These contradictory results are attributed to the time-invariant gamma distribution, which causes the trending SPI series to be identical to the rainfall series, and the time-varying gamma distribution, which results in the trend-free NSPI series. The modeling of nonstationarity in rainfall series in the proposed calculation framework depends on the purposes of the analysis since different information is revealed for drought assessments.